For a prime to be delicate as per the definition given, all numbers with "levhensthein distance" 1 must be composite. This puts a lot of conditions on what the

For a prime to be delicate as per the definition given, all numbers with "levhensthein distance" 1 must be composite. This puts a lot of conditions on what the prime can be, for p = a_0 + a_1 b + a_2 b^2 + ... + a_n b^n, if p is delicate then (p - a_0), (p - a_0 + 1), ..., (p - a_0 + b - 1) must all be composite, and so must be (p - b a_1), ..., (p - b a_1 + b (b-1)), and so forth. This is equivalent to proving that certain slices of some arithmetic successions contain no primes. Not a professional mathematician and I didn't read the paper, but I suspect this is related to prime gaps works by Tao, who is cited in the article.